EXISTENCE OF SOLUTION OF A COUPLED PROBLEM ARISING IN THE THERMOELECTRICAL SIMULATION OF ELECTRODES

In this paper we prove the existence of a solution to a system of partial differential equations arising from the thermoelectrical modeling of electrodes for electric furnaces. It consists of Maxwell equations coupled with the heat transfer equation through the Joule effect and the fact that thermal...

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Bibliographic Details
Published in:Quarterly of applied mathematics 1999-12, Vol.57 (4), p.621-636
Main Authors: BERMÚDEZ, ALFREDO, MUÑOZ-SOLA, RAFAEL
Format: Article
Language:English
Subjects:
Boundary conditions
Curl
Electric current
Electrodes
Furnaces
Graphite
Heat equation
Magnetic fields
Silicon
Thermoelectric power generation
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Summary:In this paper we prove the existence of a solution to a system of partial differential equations arising from the thermoelectrical modeling of electrodes for electric furnaces. It consists of Maxwell equations coupled with the heat transfer equation through the Joule effect and the fact that thermal conductivity and electrical resistivity depend on temperature. The problem is formulated in cylindrical coordinates to take advantage of its axisymmetry. The result is shown by introducing a regularized problem and using Schauder's fixed point theorem. Passing to the limit requires a priori estimates in weighted Sobolev spaces for an elliptic problem involving a right-hand side that is only integrable.
ISSN:0033-569X
1552-4485
DOI:10.1090/qam/1724296